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gwendallinesikes
20.09.2019 •
Mathematics
If cosθ=3/5 and θ is in quadrant iv, sin2θ=?
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Ответ:
-![\frac{24}{25}](/tpl/images/0246/9639/898a8.png)
Step-by-step explanation:
Using the double angle identity
sin2x = 2sinxcosx and
sin²x + cos²x = 1 ⇒ sinx = ±![\sqrt{1-cos^2x}](/tpl/images/0246/9639/b94a2.png)
Since Θ is in fourth quadrant then sinΘ < 0
sinΘ =-![\sqrt{1-(3/5)^2}](/tpl/images/0246/9639/c93d7.png)
= -![\sqrt{1-9/25}](/tpl/images/0246/9639/de1a3.png)
= -![\sqrt{25/25-9/25}](/tpl/images/0246/9639/33ba6.png)
= -
= - ![\frac{4}{5}](/tpl/images/0246/9639/96611.png)
Hence
sin2Θ = 2 × -
×
= - ![\frac{24}{25}](/tpl/images/0246/9639/898a8.png)
Ответ:
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